The possible dimensions are -7 and -8 units.
Solution:
Area of the rectangular skateboard park = [tex]x^{2}+15 x+56[/tex]
To find the dimensions of the park.
Let us factor the polynomial:
[tex]x^{2}+15 x+56=0[/tex]
15x can be written as 7x + 8x.
[tex]x^{2}+7 x+8x+56=0[/tex]
[tex](x^{2}+7 x)+(8x+56)=0[/tex]
Take x common in 1st two terms and 8 common in next two terms.
[tex]x(x+7 )+8(x+7)=0[/tex]
Make sure that the remaining terms in the bracket should be equal.
Now, take the common term (x + 7) outside from both terms.
[tex](x+7)(x+8)=0[/tex]
[tex]x+7=0 \ \text{or} \ x + 8 = 0[/tex]
[tex]x=-7 \ \text{or} \ x = -8[/tex]
If the length of the park is -7 then the width is -8.
If the length of the park is -8 then the width is -7.
The possible dimensions are -7 and -8 units.
